Because the concept of the "21st century AD" is less useful than that of the "century of the 2000s" (or 2100x or whatever). It's entirely arbitrary.
To an excellent first approximation the only interesting thing about the starting date of the 21st century is bragging rights: "I know there was no Year Zero. Nyah!" It has no religious significance (even if it mattered exactly when He was born, Christ wasn't born in the Year 1.) It has no geological or meteorological significance. Nor astronomical, nor geopolitical, nor legal. (Possibly astrological?) It barely has any historical significance since AD dating wasn't used in the ancient world.
Because we're people and as such have a unremitting lust for round numbers, we mark anniversaries that are round when expressed in base 10 (and why has that any special significance?) so they end in zeros or are simple fractions of numbers which end in zeroes.
For most people the date odometer turning over from --99 to --00 feels a lot more significant than the count-of-years-elapsed-since-the-Year-One passing --99.
(It's true that people speak of things like the "nineteenth century" but I suspect most people, if they have to think about what years that was, follow the algorithm "Well, let's see, it ought to be the century of the 1900s, but I gotta remember to subtract one. Ok, the century of the 1800s." If it weren't for the widespread use of things like "the Sixteenth Century" to denote historical eras, the distinction would be limited to the occasional trivia contest.)